3.1 Sunspot umbra and umbral dots

3.1.1 Central and peripheral umbral dots

Umbral dots appear as small-scale regions of enhanced brightness within the umbral core (see Figure 20View Image). Sizes and lifetimes of umbral dots have been extensively discussed in the literature. The current consensus points towards a large selection bias. Although it is clear that umbral dots are detected at spatial scales smaller than 1” and temporal scales larger than 2 minutes, it is not well established whether they posses a typical size or lifetime, since more and more are detected as the spatial resolution of the observations increases (Sobotka and Hanslmeier, 2005; Riethmüller et al., 2008bJump To The Next Citation Point).

Traditionally, umbral dots have been sub-categorized in central (CUDs) and peripheral umbral dots (PUDs) (Loughhead et al., 1979; Grossmann-Doerth et al., 1986Jump To The Next Citation Point). This distinction is based upon the location of the umbral dots: CUDs appear mostly close to the darkest region of the umbra, whereas PUDs appear commonly at the umbral and penumbral boundary. Although sometimes disputed (see, e.g., Sobotka et al., 1997), there are many works that claim that these two families of umbral dots posses very different proper motions (Molowny-Horas, 1994; Sobotka et al., 1995Jump To The Next Citation Point; Riethmüller et al., 2008b; Watanabe et al., 2009a), with the peripheral ones exhibiting the largest velocities and apparently being related to inner bright penumbral grains. The physical similarities between peripheral umbral dots and penumbral grains have been studied by Sobotka and Jurčák (2009).

3.1.2 Thermal and magnetic structure of umbral dots

The large continuum intensities, as compared to the umbral dark surroundings, immediately implies (see, for example, Section 2.5) that the temperature in umbral dots at τc = 2∕3 is larger than the temperature at the same layer in the umbral background. Old and current estimates all coincide in a temperature difference that ranges from 500 K (Grossmann-Doerth et al., 1986; Riethmüller et al., 2008aJump To The Next Citation Point) up to 1500 K (Tritschler and Schmidt, 1997Jump To The Next Citation Point; Socas-Navarro et al., 2004Jump To The Next Citation Point). This temperature difference almost vanishes about 200 – 250 km above τc = 1: see Figure 8 in Socas-Navarro et al. (2004Jump To The Next Citation Point), and Figure 4 in Riethmüller et al. (2008aJump To The Next Citation Point), which is reproduced here (in Figure 21View Image).

The strength of the magnetic field inside umbral dots has been a somewhat controversial subject, with some works finding no large differences between umbral dots and the umbral background (Lites et al., 1989; Tritschler and Schmidt, 1997), and other works finding a clear reduction of the field strength both in central and peripheral umbral dots (Wiehr and Degenhardt, 1993; Socas-Navarro et al., 2004Jump To The Next Citation Point; Riethmüller et al., 2008aJump To The Next Citation Point). However, as pointed out by the the latter works this could again be τ-dependent, with the differences in the magnetic field being small a few hundred kilometers above τc = 1, but fairly large close to this level. Here the difference can be such that the magnetic field inside the umbral dot is only a few hundred Gauss (see Figure 21View Image). The inclination of the magnetic field ζ has been found to be only slightly larger than in the mean umbral background (see Figure 8 in Socas-Navarro et al., 2004Jump To The Next Citation Point, and Figure 4 in Bharti et al., 2009), which is itself very much vertical (see Figures 7View Image and 11View Image). This will be a recurrent topic in future sections (Sections 3.2.5, 3.2.7, and 3.2.6) when discussing the differences/similarities between umbral dots, penumbral filaments, and light bridges.

The smaller field strengths inside umbral dots leads to an enhanced gas pressure as compared to the surrounding umbra. This is consistent with the larger temperatures found inside UDs. These numbers can be employed to derive a Wilson depression of about 100 – 200 km, that is, the τc = 1 level is formed about 100 – 200 km higher in umbral dots than in the surrounding umbra (Socas-Navarro et al., 2004Jump To The Next Citation Point). This value is similar to the height difference for the continuum level between penumbral spines and intraspines (see Figure 9View Image). This has important consequences because the measured differences in the thermal and magnetic structure correspond to τc = 1. If the continuum level is actually formed higher (in the geometrical height scale) inside UDs than in the umbra, this means that the differences, if measured at the same geometrical height, would be much larger than the numbers previously cited. This effect applies indeed, not only to umbral dots, but also in any other structure in the solar photosphere that is elevated with respect to its surroundings. Note also that the Wilson depression between the umbra and umbral dots can be inferred from purely geometrical considerations of sunspot observations close to the limb (Lites et al., 2004; Watson et al., 2009).

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Figure 21: Vertical stratification (in optical depth τc-scale) of the temperature (left panel) and the total magnetic field strength (right panel). The blue curves shows the stratification for the diffuse umbral background, where the red curves correspond to the vertical stratification along an umbral dot. Close to the continuum, τc = 1, the umbral dot is much hotter and possesses a weaker magnetic field than the umbra. These differences disappear about 100 – 200 km higher in the photosphere: log τc ∼ − 2 (from Riethmüller et al., 2008a, reproduced by permission of the AAS).

Note that, the presence of regions inside the sunspot umbra where the magnetic field is strongly reduced and the temperature and gas pressure enhanced around τc = 1, goes along the same lines as Section 2.4, where we concluded that close to the continuum level the plasma-β is larger than unity. As explained in Sect 2.3 this leads to non-potential configurations for the sunspot magnetic field because the convective motions are strong enough to drag and twist the magnetic field lines.

3.1.3 Signatures of convection in umbral dots

As mentioned in Section 3.1, there must exist some form of convection operating in the umbra of sunspots. The main candidate for this are the umbral dots. This was motivated by the fact that umbral dots show enhanced brightness with respect to the umbral background and, therefore, must be heated more efficiently. In addition, numerical simulations of umbral magneto-convection (Schüssler and Vögler, 2006Jump To The Next Citation Point) predict the existence of upflows at the center of umbral dots and downflows at its edges. As it occurs in the case of penumbral filaments (see Section 3.2.4), the search for convective-like velocity patterns in umbral dots has been hindered by the limited spatial resolution of the observations. For instance, while upflows ranging from 0.4 – 1.0 km s–1 at the center of umbral dots have been known for quite some time (Rimmele, 2004; Socas-Navarro et al., 2004; Watanabe et al., 2009b), downflows have been much more difficult to detect. However, in the past few years there have been a few positive detections of downflows at the edges of umbral dots (Bharti et al., 2007; Ortiz et al., 2010Jump To The Next Citation Point). The latter work presents evidence that supports the numerical simulations of umbral convection in great detail, with umbral dots that show upflows along their central dark lane and strong downflows at the footpoints of the dark lanes (see Figure 3 in Ortiz et al., 2010Jump To The Next Citation Point). This agreement is evident if we compare the observations from Ortiz et al. (2010Jump To The Next Citation Point) in Figure 22View Image with the simulations from Schüssler and Vögler (2006Jump To The Next Citation Point) in Figure 23View Image.

The lower magnetic field inside umbral dots mentioned in Section 3.1.2 is a direct consequence of the convective motions described here. In the sunspot umbra, convective motions push the magnetic field lines towards the boundary of the convective cell, thereby creating a region where the vertical component of the magnetic field vector is strongly reduced. Since the ambient magnetic field is vertical, this automatically yields a very small field inside the umbral dot. At the top of the convective cell the magnetic field forms a cusp or canopy, preventing the material from continuing to flow upwards. The pile-up of material at this point creates a region of locally enhanced density, which is responsible for the appearance of the central dark lane inside umbral dots (Schüssler and Vögler, 2006Jump To The Next Citation Point).

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Figure 22: Results from spectropolarimetric observations. Left panel: continuum intensity map inside the umbra of a sunspot. The circles denote the location of several umbral dots (see as intensity enhancements; see also 20View Image). The largest circle encircles two large umbral dots that show prominent central dark lanes. Right panel: map of the line-of-sight velocity in deep layers. This map shows an upflow (blueshift) along the central dark lane and downflows (redshift) at the footpoints of the dark lane (from Ortiz et al., 2010, reproduced by permission of the AAS).
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Figure 23: Results from 3D MHD simulations. Left panel: continuum intensity in the umbra of a sunspot. Right panel: map of the line-of-sight velocity. This panel shows upflows (blueshift) along the central dark lane of umbral dots. Downflows (redshift) are also visible all around the central dark lane, although they are stronger at the footpoints of the dark lane (from Schüssler and Vögler, 2006Jump To The Next Citation Point, reproduced by permission of the AAS).

3.1.4 Light bridges

Besides umbral dots, the most striking manifestation of convection in the umbra appears in the form of light bridges. These are elongated bright features that often split the umbra in two sections connecting two different sides of the penumbra (see Figure 20View Image). Light bridges and umbral dots share many similarities. For instance, both feature a central dark lane and bright edges. Indeed, light bridges can be considered as an extreme form of elongated umbral dots. Their larger sizes have actually allowed for the detection of both blue and redshifted velocities with only a moderate spatial resolution of 1” (Sobotka et al., 1995; Leka, 1997; Rimmele, 1997).

Recent observations at much better spatial resolution have also been able to establish a clear connection between upflows and the central dark lane in light bridges, as well as downflows and the bright edges of the light bridge (Hirzberger et al., 2002; Berger and Berdyugina, 2003; Rouppe van der Voort et al., 2010). In addition, as it also occurs with umbral dots (see Section 3.1.2), the magnetic field is weaker and slightly more inclined in light bridges as compared to the surrounding umbra (Beckers and Schröter, 1969b; Rueedi et al., 1995; Jurčák et al., 2006). The nature of the central dark lane in light bridges is the same as in umbral dots (Section 3.1.3).

3.1.5 Subsurface structure of sunspots: cluster vs. monolithic models

The presence of several convective features in the umbra of sunspots immediately posses the question of whether the convective upflows and downflows in umbral dots and light bridges extend deep into the solar interior or, on the contrary, are only a surface effect. Two distinct theoretical models are usually cited to showcase these two possibilities: the cluster model (Parker, 1979) and the monolithic model (Gokhale and Zwaan, 1972; Meyer et al., 1974, 1977). In both cases, convective upflows at the plume’s center reach the photosphere, where they lose their energy via radiative cooling and sink back into the Sun at the edges of the umbral dots or light bridges. In the monolithic model the vertical extension of the plumes is small, leading to a situation in which the plume is completely surrounded by the sunspot’s magnetic field. However, in the cluster model convective plumes reach very deep into the solar interior, connecting with field-free convection zone below the sunspot. In the latter model, what appears as a single flux tube in the photosphere splits into many smaller flux tubes deeper down, leaving intrusions of field-free plasma in between the smaller tubes. Inside this intrusions is where the convection takes place.

It is not possible to distinguish between these two models employing spectropolarimetric observations because, below τc = 1, the plasma is so opaque that no photon can travel from that depth without being absorbed. Currently, the only observational tool at our disposal that can allow us to infer the subsurface structure of sunspots is local helioseismology (Gizon and Birch, 2005; Moradi et al., 2010). Although this technique is still under development, it will hopefully shed some light on this subject in the near future.

An alternative way of studying the subsurface structure of sunspots is by means of numerical simulations of solar magneto-convection. Some recent studies (Schüssler and Vögler, 2006Jump To The Next Citation Point) show that convection can occur in the umbra in the form of plumes that do not reach more than 1 Mm beneath the solar surface. These convective plumes are completely surrounded by the sunspot’s magnetic field and manifest themselves in the photosphere in the form of umbral dots. Furthermore, they also transport sufficient amounts of energy as to account for the observed umbral brightness (see Sections 2.5 and 3.1; see also Figure 23View Image): 10 – 30% of the quiet Sun. At first glance these simulations seem to lend support to the monolithic sunspot model. However, the depth of the simulation box in Schüssler and Vögler (2006) is only 1.6 Mm. New simulations with deeper domains have been presented by Rempel (2011Jump To The Next Citation Point) and Cheung et al. (2010Jump To The Next Citation Point), with boxes of 6.1 and 8.2 Mm depth, respectively. In these new simulations, umbral dots present a very similar topology as with shallower boxes. However, light bridges appear to be rooted very deep, with convective plumes that reach more than 2 Mm into the Sun (see, for example, Figure 12 in Cheung et al., 2010). Further work is, therefore, needed since the current simulations are not sufficient to completely rule out the cluster model.

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